Question: Can this differential equation be solved using separation of variables? $\dfrac{dy}{dx}=10-2y+9x$ Choose 1 answer: Choose 1 answer: (Choice A) A Yes (Choice B) B No
Solution: For an equation to be solvable using separation of variables, we need to be able to bring it to the form $\dfrac{dy}{dx}=f(x)g(y)$. In this form, $f(x)$ doesn't include $y$ and $g(y)$ doesn't include $x$. Notice that we must multiply, not add, $f(x)$ and $g(y)$. It's not possible to factor $10-2y+9x$ as the product of two such expressions. Therefore, it isn't possible to bring the equation to the form $\dfrac{dy}{dx}=f(x)g(y)$. No, the equation cannot be solved using separation of variables.